Question

A particle is at $x=+5m$ at $t=0$, $x=-7m$ at $t=6s$ and $x=+2m$ at $t=10s$. The average velocity of the particle during the intervals:
(a) $t=0$ to $t=6s$
(b) $t=6s$ to $t=10s$
(c) $t=0$ to $10s$
is respectively :

• A. $-2{ms}^{-1},2.25{ms}^{-1},-0.3{ms}^{-1}$
• B. $2{ms}^{-1},2.25{ms}^{-1},-0.3{ms}^{-1}$
• C. $0.3{ms}^{-1},-0.3{ms}^{-1},-2{ms}^{-1}$
• D. $2.25{ms}^{-1},-0.3{ms}^{-1},-2{ms}^{-1}$

Answer 1

The correct option is A $-2{ms}^{-1},2.25{ms}^{-1},-0.3{ms}^{-1}$

$V_{avg}\left(0to6\right)=\frac{x_2-x_1}{t_2-t_1}=\frac{-7-\left(5\right)}{6-0}=\frac{-12}{6}=-2m/s$

$V_{avg}\left(6to10\right)=\frac{x_3-x_2}{t_3-t_2}=\frac{2-(-7)}{10-6}=\frac{9}{4}=2.252m/s$

$V_{avg}\left(0to10\right)=\frac{x_3-x_1}{t_3-t_1}=\frac{2-5}{10-0}=\frac{-3}{10}=-0.3m/s$